A New Stochastic Approximation Method for Gradient-based Simulated Parameter Estimation
Zehao Li, Yijie Peng
TL;DR
This work tackles parameter estimation when the likelihood is inaccessible by introducing gradient-based simulated parameter estimation (GSPE) built on multi-time-scale stochastic approximation to remove ratio bias from gradient estimators. By employing unbiased GLR estimators for likelihood components and coupling two time scales, the method yields bias-free updates for MLE and PDE settings, and extends to HMMs through particle filtering and IPA-style gradients. The framework includes a nested, outer-inner simulation structure for PDE (ELBO gradients under variational inference) and a two-tier update scheme (outer parameter updates and inner gradient trackers) that reduces variance and computational cost. Empirical results across MLE, PDE, and HMM tasks demonstrate substantial bias reduction and competitive runtimes, illustrating GSPE's potential for robust parameter calibration in challenging stochastic environments where analytical likelihoods are unavailable.
Abstract
This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation framework, which employs a multi-time scale stochastic approximation algorithm. This approach effectively addresses the ratio bias that arises in both maximum likelihood estimation and posterior density estimation problems. The proposed algorithm enhances estimation accuracy and significantly reduces computational costs, as demonstrated through extensive numerical experiments. Our work extends the GSPE framework to handle complex models such as hidden Markov models and variational inference-based problems, offering a robust solution for parameter estimation in challenging stochastic environments.